https://www.youtube.com/watch?v=B6u-FPskfAE

This is not intuitive to me. It seems like a "new idea" is something that (almost by definition) isn't in the training set. Can you elaborate a bit?

Edit: but perhaps a good model could arise from training, which would be a good idea in the sense that parsimonious ideas are good scientific ideas.

You can, actually! Any compressor can be losslessly converted into a generator, and vice versa.

Traditional compressors like gzip are of course very simple and can only replicate rough patterns from the input. But they are technically doing the same thing.

Given a context (for LLMs, this would include the entire pretraining dataset, plus the prompt), you compress `context + next_token` for every possible next token. The tokens that co-compress best with the existing context are the 'least surprising' continuations. Choose one of them and iterate.

You can easily generate text with gzip this way. It won't be very good text, because gzip compression is not as sophisticated as a transformer + SGD, but the principle is the same.

Makes me wonder idly, - is this conceptually akin in some sense to a "universal grammar," and if so - with a broad enough training set, is there a latent durable universal grammar that might be similarly recovered and injected to the benefit of all training, - does that grammar go beyond morphological/syntactical/grammatical features, into e.g. semantics and pragmatics